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Encyclopedia > Locus (mathematics)

In mathematics, a locus (Latin for "place", plural loci) is a collection of points which share a common property. A locus of points usually forms a continuous figure or figures. For example, a line is the locus of points equidistant from two fixed points. Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ... Latin is an ancient Indo-European language originally spoken in the region around Rome called Latium. ... A spatial point is an entity with a location in space but no extent (volume, area or length). ... A line, or straight line, can be described as an (infinitely) thin, (infinitely) long, perfectly straight curve (the term curve in mathematics includes straight curves). In Euclidean geometry, exactly one line can be found that passes through any two points. ... personal space, proxemics. ...

The conic sections may be defined in terms of loci: In mathematics, a conic section (or just conic) is a curved locus of points, formed by intersecting a cone with a plane. ...

• A circle is the locus of points from which the distance to the center is a given value, the radius.
• An ellipse is the locus of points, the sum of the distances from which to the foci is a given value.
• A hyperbola is the locus of points, the difference of the distances from which to the foci is a given value.
• A parabola is the locus of points, the distances from which to the focus and to the directrix are equal.

Very complex geometric shapes may described as the locus of zeros of a function or polynomial. Thus, for example, the quadric surfaces are defined as the loci of zeros of the quadratic polynomials. More generally, the locus of zeros of a set of polynomials are called an algebraic variety, the properties of which are studied in the branch of mathematics known as algebraic geometry. In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed point, the centre. ... The distance between two points is the length of a straight line segment between them. ... In classical geometry, a radius of a circle or sphere is any line segment from its center to its boundary. ... The ellipse and some of its mathematical properties. ... In geometry, the focus (pl. ... A graph of a hyperbola, where h = k = 0 and a = b = 2. ... Wikisource has an original article from the 1911 EncyclopÃ¦dia Britannica about: Parabola A parabola The parabola (from the Greek: Ï€Î±ÏÎ±Î²Î¿Î»Î®) is a conic section generated by the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. ... In mathematics, a conic section (or just conic) is a curved locus of points, formed by intersecting a cone with a plane. ... In mathematics, a root (or a zero) of a function f is an element x in the domain of f such that f(x) = 0. ... Partial plot of a function f. ... In mathematics, a polynomial is an expression in which constants and variables are combined using only addition, subtraction, multiplication, and positive whole number exponents (raising to a power). ... This is an article about quadric in mathematics, to see the computing company go to Quadrics. ... f(x) = x2 - x - 2 In mathematics, a quadratic function is a polynomial function of the form , where a is nonzero. ... In classical algebraic geometry (and to some extent also in modern algebraic geometry), the main objects of study are algebraic varieties. ... Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. ...

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 Locus (mathematics) - guideofcasinos.com (208 words) A circle is the locus of points from which the distance to the center is a given value, the radius. An ellipse is the locus of points, the sum of the distances from which to the foci is a given value. A parabola is the locus of points, the distances from which to the focus and to the directrix are equal.
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